Lecture 16: Voting systems Economics 336 Economics 336 (Toronto) Lecture 16: Voting systems 1 / 18
Introduction Last lecture we looked at the basic theory of majority voting: instability in voting: Condorcet paradox single peaked preferences and median voter equilibrium representative democracy and Hotelling equilibrium In this lecture, we examine the properties of a number of real-world voting systems. Is median voter theory a good description of reality? Are there other voting systems that would do better than our current system? Economics 336 (Toronto) Lecture 16: Voting systems 2 / 18
Problems with the median voter model Key simplifying assumptions of the Hotelling model: 1 single dimension issue space proof requires single-peaked preferences voters care about many issues median voter equilbrium fails in multiple dimensions most elections fought on a small number of issues but which? 2 two parties In reality, often three or more viable candidates no Nash equilibrium with more than two candidates. (Why not?) Economics 336 (Toronto) Lecture 16: Voting systems 3 / 18
3 office-seeking candidates Hotelling assumes parties only want to win leads to convergence what if parties care about policy/ideology? 4 no abstentions in Canada, only 40-60% voter turnout how does turnout game affect politics? 5 perfect information and perfect commitment to promises another role for elections: evaluating past performance 6 no other means of influencing policy legislative bargaining lobbying activities role of campaign contributions Economics 336 (Toronto) Lecture 16: Voting systems 4 / 18
Empirical evidence I Support for the median voter hypothesis is mixed. 1 Do democracies behave differently than dictatorships? Median voter model suggests they should tax, spend more. Mulligan, Gil and Sala-i-Martin (JEP, 2004) examine this with cross-country evidence. Cross-country regressions show that democracies do not spend more, or tax more progressively, than dictatorships suggesting that elections are unimportant. Problems with this methodology? Economics 336 (Toronto) Lecture 16: Voting systems 5 / 18
Alternative approach: Case study methodology. Compare spending growth in 3 countries that transitioned to democracies in 1970s (Greece, Spain, Portugal) to a similar one (Italy) that was always democratic. Government share increases. (Implications?) Economics 336 (Toronto) Lecture 16: Voting systems 6 / 18
Empirical evidence II (skip) 2 Husted and Kenny (JPE, 1997) look at effects of repeal of Jim Crow laws disenfranchising African Americans, 1964 70. poll taxes made it harder for poor, especially blacks, to vote. literacy tests were asymmetrically applied to whites and blacks. Repealed following 1965, 1970 Voting Rights Acts. Arguably, this change gives a better estimate of the causal effect of voting, because it was imposed from above. (Why?) Results: turnout increased most in poor counties of South following repeal; share of state spending on welfare spending for poor rose 11.8% (relative to change in other states) following repeal of poll taxes. (Literacy tests insignificant.) Economics 336 (Toronto) Lecture 16: Voting systems 7 / 18
Empirical evidence III 3 Do elected representatives really act on behalf of median voter, as in Hotelling model? Lee, Moretti and Butler (QJE, 2004) compare voting records of Democratic and Republican congressman, 1946-95. Under median voter hypothesis, representatives of both parties should behave the same if they represent a median voter with the same preferences. How to test this? can t just compare average Democrat to average Republican more liberal (conservative) districts are more likely to have a Democratic (Republican) congressman not the same people instead compare districts where Democrat share is 50-52% to those where it is 48-50% this is a regression discontinuity design Economics 336 (Toronto) Lecture 16: Voting systems 8 / 18
Interpreting the figure: ADA score is a standard measure of liberal voting in Congress jump in score when Democrat elected is a failure of the median voter model possible explanations: candidates election promises do not converge to the median incumbents realize they are safe after first elected and can ignore election promises and vote how they like Economics 336 (Toronto) Lecture 16: Voting systems 9 / 18
Other voting rules I. Plurality rule A single round of voting on all alternatives. It is reasonable to think we should choose a Condorcet winner when one exists. But: voter 1 2 3 first choice A B C second choice B A A third choice C C B number 2 3 4 Which is plurality winner? Condorcet winner? Plurality rule elicits too little information: potential for vote splitting and strategic voting. Economics 336 (Toronto) Lecture 16: Voting systems 10 / 18
Example: Voting for a name In 1970, the Ontario cities of Fort William and Port Arthur were amalgamated, and voters were asked to choose a new name in a plurality-rule plebiscite. Three alternatives were on the ballot, and the votes were: Alternative votes The Lakehead 8,477 Lakehead 15,302 Thunder Bay 15,831 If a runoff system had been used, which do you think would have won? Economics 336 (Toronto) Lecture 16: Voting systems 11 / 18
Other voting rules II. Alternative voting Under alternative voting (AV) systems, voters submit a ranking of all candidates, not just a first choice. A winner is chosen by sequential counting. (Also called single transferable vote or instant runoff voting.) 1 First place votes are counted. 2 If one candidate has a majority of votes, it is declared the winner and counting stops. 3 If not, the candidate with the fewest votes is eliminated, and these ballots next preferences are added to totals from step 1. 4 Counting continues from step 2. Many people think we should adopt AV in place of our plurality rule elections. What advantages can you see to AV? Economics 336 (Toronto) Lecture 16: Voting systems 12 / 18
Exercise on AV Consider again the voting for a name example: voter 1 2 3 first choice A B C second choice B A A third choice C C B number 2 3 4 1 If voters are sincere, what is the outcome under AV? Is it the Condorcet winner? 2 If voters behave strategically, analyze the likely outcomes (equilibria) under plurality rule and under AV. Economics 336 (Toronto) Lecture 16: Voting systems 13 / 18
Other voting rules III. Borda voting Borda voting is a weighted voting scheme, where voters allocate scores to the alternatives. For example, let the voter s score for each alternative be his or her rank for the alternative. The Borda rule winner is then the alternative with the smallest overall aggregate score. Borda voting makes it more likely compromise candidates will win, since voters report their ranking of all alternatives, not just their preferred alternative. But it still does not allow people to communicate intensity of preferences. Economics 336 (Toronto) Lecture 16: Voting systems 14 / 18
In our first example, let the distribution of preference types be voter 1 2 3 first choice A B C second choice B C A third choice C A B number of voters 3 2 2 (Is there a Condorcet winner? When there is, will Borda choose it?) Borda scores are: S A = 3 1+2 3+2 2 = 13 S B = 3 2+2 1+2 3 = 14 S C = 3 3+2 2+2 1 = 15 so A wins. Economics 336 (Toronto) Lecture 16: Voting systems 15 / 18
Borda rule gives a unique winner, and in this example it seems sensible. But now suppose we add a fourth alternative such that: Borda scores are now: voter 1 2 3 first choice A B C second choice B C A third choice C D B fourth choice D A D number of voters 3 2 2 S A = 3 1+2 4+2 2 = 15 S B = 3 2+2 1+2 3 = 14 S C = 3 3+2 2+2 1 = 15 S D = 3 4+2 3+2 4 = 26 The presence of option D on the ballot changes the winner, even though D is not chosen. This seems undesirable. Economics 336 (Toronto) Lecture 16: Voting systems 16 / 18
Other voting rules III. Score voting One problem with all these systems is they ask voters about rankings, but not about how much they care. This leaves out important information, and it leads to some of these paradoxes. (Think of the voting for a name example.) Other voting systems would ask voters about intensity of preference, e.g.: score voting: each voter can allocate 100 points among candidates in any way highest score is winner approval voting: each voter can vote yes or no on all candidates most yes votes is winner (a special case of score voting) negative plurality: each voter can name candidate that is least preferred lowest score is winner (a special case of approval voting) How would these systems work in the voting for a name example? Economics 336 (Toronto) Lecture 16: Voting systems 17 / 18
Arrow s impossibility theorem Ken Arrow (1951) asked whether there was any voting scheme (way of aggregating rankings) that leads to consistent, rational social choices, i.e. complete ranking: it gives a complete social ordering of alternatives, with no Condorcet cycles (e.g. no pairwise voting) unanimity: it ranks higher any alternative that is preferred by all voters to another (e.g. no non-welfarist rules) independence of irrelevant alternatives: the ranking of any two alternatives does not depend on whether some third alternative is available or not (e.g. no Borda rule) Arrow showed that, if there are more than 2 voters and more than 2 alternatives, there the only such voting scheme gives all the votes to a single person i.e. a dictatorship. This is probably undesirable! There is no perfect voting rule. Economics 336 (Toronto) Lecture 16: Voting systems 18 / 18